Detailed conclusion table per each integral is given by the table below. The elapsed time is in seconds. For failed result it is given as F(-1) if the failure was due to timeout. It is given as F(-2) if the failure was due to an exception being raised, which could indicate a bug in the system. If the failure was due to integral not being evaluated within the time limit, then it is given as F.
In this table, the column N.S.
means normalized size and is defined as \(\frac {\text {antiderivative leaf size}}{\text {optimal antiderivative leaf size}}\). To make the table
fit the page, the name Mathematica
was abbreviated to MMA
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 15 | 15 | 15 | 14 | 14 | 14 | 14 | 17 | 14 |
N.S. |
1 | 0.68 | 0.68 | 0.68 | 0.64 | 0.64 | 0.64 | 0.64 | 0.77 | 0.64 |
time (sec) |
N/A | 0.295 | 0.013 | 0.514 | 0.112 | 0.083 | 0.148 | 0.111 | 0.186 | 2.903 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | B | F(-1) | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 19 | 16 | 42 | 42 | 0 | 0 | 37 | 0 |
N.S. |
1 | 0.00 | 1.00 | 0.84 | 2.21 | 2.21 | 0.00 | 0.00 | 1.95 | 0.00 |
time (sec) |
N/A | 0.000 | 1.289 | 1.071 | 1.034 | 0.080 | 0.000 | 0.000 | 0.187 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 22 | 22 | 19 | 18 | 32 | 19 | 18 | 30 | 18 |
N.S. |
1 | 1.00 | 1.00 | 0.86 | 0.82 | 1.45 | 0.86 | 0.82 | 1.36 | 0.82 |
time (sec) |
N/A | 0.183 | 0.029 | 0.099 | 0.113 | 0.084 | 0.083 | 0.114 | 0.192 | 2.618 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 38 | 34 | 31 | 31 | 0 | 0 | 38 | 189 |
N.S. |
1 | 0.00 | 1.27 | 1.13 | 1.03 | 1.03 | 0.00 | 0.00 | 1.27 | 6.30 |
time (sec) |
N/A | 0.000 | 0.394 | 4.373 | 0.304 | 0.098 | 0.000 | 0.000 | 2.599 | 3.179 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 35 | 15 | 13 | 12 | 12 | 10 | 20 | 34 | 13 |
N.S. |
1 | 2.33 | 1.00 | 0.87 | 0.80 | 0.80 | 0.67 | 1.33 | 2.27 | 0.87 |
time (sec) |
N/A | 0.162 | 0.009 | 0.207 | 0.029 | 0.083 | 0.071 | 0.111 | 0.187 | 2.642 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | B | A | F(-1) | F | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 28 | 57 | 59 | 27 | 0 | 0 | 28 | 0 |
N.S. |
1 | 0.00 | 1.00 | 2.04 | 2.11 | 0.96 | 0.00 | 0.00 | 1.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.274 | 0.114 | 0.587 | 0.091 | 0.000 | 0.000 | 0.434 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 26 | 17 | 13 | 8 | 13 | 28 | 25 |
N.S. |
1 | 0.00 | 1.00 | 1.00 | 0.65 | 0.50 | 0.31 | 0.50 | 1.08 | 0.96 |
time (sec) |
N/A | 0.000 | 0.095 | 1.239 | 0.036 | 0.089 | 0.060 | 0.162 | 0.185 | 2.848 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | B | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 30 | 22 | 19 | 67 | 39 | 19 | 39 | 23 | 28 |
N.S. |
1 | 1.20 | 0.88 | 0.76 | 2.68 | 1.56 | 0.76 | 1.56 | 0.92 | 1.12 |
time (sec) |
N/A | 0.345 | 1.362 | 0.582 | 0.090 | 0.078 | 0.068 | 0.117 | 0.194 | 0.078 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 25 | 24 | 28 | 25 | 24 | 28 | 28 | 28 |
N.S. |
1 | 0.00 | 1.00 | 0.96 | 1.12 | 1.00 | 0.96 | 1.12 | 1.12 | 1.12 |
time (sec) |
N/A | 0.000 | 0.198 | 2.059 | 0.164 | 0.080 | 0.151 | 0.175 | 0.356 | 3.393 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 74 | 26 | 32 | 32 | 32 | 29 | 32 | 33 | 25 |
N.S. |
1 | 2.39 | 0.84 | 1.03 | 1.03 | 1.03 | 0.94 | 1.03 | 1.06 | 0.81 |
time (sec) |
N/A | 2.970 | 1.474 | 0.446 | 0.071 | 0.078 | 0.057 | 0.114 | 0.352 | 0.083 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 76 | 79 | 68 | 60 | 56 | 66 | 58 | 74 | 57 |
N.S. |
1 | 4.22 | 4.39 | 3.78 | 3.33 | 3.11 | 3.67 | 3.22 | 4.11 | 3.17 |
time (sec) |
N/A | 0.286 | 0.049 | 1.145 | 0.032 | 0.095 | 0.102 | 0.110 | 0.320 | 0.066 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 17 | 15 | 17 | 18 | 27 | 15 | 13 | 26 | 13 |
N.S. |
1 | 0.71 | 0.62 | 0.71 | 0.75 | 1.12 | 0.62 | 0.54 | 1.08 | 0.54 |
time (sec) |
N/A | 0.224 | 0.011 | 0.162 | 0.026 | 0.077 | 0.088 | 0.120 | 0.208 | 0.033 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 19 | 17 | 15 | 25 | 14 | 15 | 14 | 18 | 14 |
N.S. |
1 | 1.12 | 1.00 | 0.88 | 1.47 | 0.82 | 0.88 | 0.82 | 1.06 | 0.82 |
time (sec) |
N/A | 0.240 | 0.061 | 0.142 | 0.055 | 0.084 | 0.072 | 0.124 | 0.210 | 0.102 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 6 | 2 | 2 | 3 | 2 | 2 | 2 | 3 | 2 | 2 |
N.S. |
1 | 0.33 | 0.33 | 0.50 | 0.33 | 0.33 | 0.33 | 0.50 | 0.33 | 0.33 |
time (sec) |
N/A | 0.124 | 0.000 | 0.027 | 0.034 | 0.067 | 0.018 | 0.110 | 0.199 | 0.001 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 36 | 36 | 17 | 35 | 35 | 37 | 35 | 35 | 36 |
N.S. |
1 | 1.89 | 1.89 | 0.89 | 1.84 | 1.84 | 1.95 | 1.84 | 1.84 | 1.89 |
time (sec) |
N/A | 0.194 | 0.004 | 0.322 | 0.024 | 0.078 | 0.022 | 0.109 | 0.202 | 2.720 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 22 | 16 | 18 | 18 | 17 | 15 | 18 | 18 | 16 |
N.S. |
1 | 0.88 | 0.64 | 0.72 | 0.72 | 0.68 | 0.60 | 0.72 | 0.72 | 0.64 |
time (sec) |
N/A | 0.169 | 0.005 | 0.112 | 0.026 | 0.069 | 0.045 | 0.121 | 0.193 | 2.911 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 37 | 34 | 30 | 32 | 29 | 26 | 33 | 317 | 29 |
N.S. |
1 | 1.68 | 1.55 | 1.36 | 1.45 | 1.32 | 1.18 | 1.50 | 14.41 | 1.32 |
time (sec) |
N/A | 0.281 | 0.017 | 0.426 | 0.032 | 0.087 | 0.403 | 0.120 | 0.202 | 3.085 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 12 | 12 | 13 | 19 | 19 | 7 | 12 | 20 | 12 |
N.S. |
1 | 0.92 | 0.92 | 1.00 | 1.46 | 1.46 | 0.54 | 0.92 | 1.54 | 0.92 |
time (sec) |
N/A | 0.480 | 0.048 | 0.383 | 0.057 | 0.086 | 0.050 | 0.120 | 0.194 | 2.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 30 | 20 | 22 | 48 | 23 | 19 | 27 | 21 | 18 |
N.S. |
1 | 1.58 | 1.05 | 1.16 | 2.53 | 1.21 | 1.00 | 1.42 | 1.11 | 0.95 |
time (sec) |
N/A | 0.723 | 0.063 | 0.226 | 0.145 | 0.082 | 3.363 | 0.123 | 0.197 | 2.973 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 0 | 22 | 29 | 31 | 31 | 49 | 31 | 93 | 22 |
N.S. |
1 | 0.00 | 0.92 | 1.21 | 1.29 | 1.29 | 2.04 | 1.29 | 3.88 | 0.92 |
time (sec) |
N/A | 0.000 | 5.034 | 5.169 | 0.196 | 0.095 | 0.171 | 0.121 | 0.207 | 3.208 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 31 | 30 | 26 | 100 | 25 | 24 | 26 | 26 | 26 |
N.S. |
1 | 1.11 | 1.07 | 0.93 | 3.57 | 0.89 | 0.86 | 0.93 | 0.93 | 0.93 |
time (sec) |
N/A | 0.447 | 0.294 | 0.352 | 0.035 | 0.086 | 0.064 | 0.117 | 0.188 | 2.835 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 24 | 23 | 26 | 22 | 25 | 20 | 25 | 26 | 22 |
N.S. |
1 | 0.71 | 0.68 | 0.76 | 0.65 | 0.74 | 0.59 | 0.74 | 0.76 | 0.65 |
time (sec) |
N/A | 10.457 | 0.009 | 0.622 | 0.032 | 0.074 | 1.126 | 0.120 | 0.199 | 0.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 26 | 23 | 22 | 22 | 26 | 0 | 29 | 22 |
N.S. |
1 | 0.00 | 1.00 | 0.88 | 0.85 | 0.85 | 1.00 | 0.00 | 1.12 | 0.85 |
time (sec) |
N/A | 0.000 | 0.292 | 46.695 | 0.150 | 0.092 | 28.100 | 0.000 | 0.211 | 2.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | B | B | A | F(-1) | F(-1) | B | B |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 0 | 66 | 77 | 29 | 0 | 0 | 33 | 26 |
N.S. |
1 | 0.00 | 0.00 | 2.54 | 2.96 | 1.12 | 0.00 | 0.00 | 1.27 | 1.00 |
time (sec) |
N/A | 0.000 | 0.000 | 65.480 | 0.204 | 0.086 | 0.000 | 0.000 | 0.208 | 3.302 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | B | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 65 | 30 | 23 | 0 | 20 | 100 | 22 | 72 | 24 |
N.S. |
1 | 2.50 | 1.15 | 0.88 | 0.00 | 0.77 | 3.85 | 0.85 | 2.77 | 0.92 |
time (sec) |
N/A | 0.414 | 0.015 | 0.343 | 0.000 | 0.081 | 0.698 | 0.112 | 0.206 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 13 | 15 | 11 | 10 | 10 | 10 | 10 | 11 | 10 |
N.S. |
1 | 0.62 | 0.71 | 0.52 | 0.48 | 0.48 | 0.48 | 0.48 | 0.52 | 0.48 |
time (sec) |
N/A | 0.155 | 0.001 | 0.075 | 0.035 | 0.082 | 0.032 | 0.103 | 0.204 | 0.027 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 0 | 30 | 28 | 27 | 42 | 24 | 27 | 30 | 27 |
N.S. |
1 | 0.00 | 1.03 | 0.97 | 0.93 | 1.45 | 0.83 | 0.93 | 1.03 | 0.93 |
time (sec) |
N/A | 0.000 | 0.160 | 24.290 | 0.189 | 0.091 | 2.065 | 0.448 | 0.260 | 3.334 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 28 | 19 | 18 | 26 | 18 | 19 | 18 | 20 | 16 |
N.S. |
1 | 1.12 | 0.76 | 0.72 | 1.04 | 0.72 | 0.76 | 0.72 | 0.80 | 0.64 |
time (sec) |
N/A | 0.208 | 0.078 | 0.208 | 0.053 | 0.071 | 0.078 | 0.115 | 0.197 | 2.915 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 26 | 24 | 39 | 35 | 41 | 61 | 37 | 40 |
N.S. |
1 | 0.00 | 0.93 | 0.86 | 1.39 | 1.25 | 1.46 | 2.18 | 1.32 | 1.43 |
time (sec) |
N/A | 0.000 | 0.607 | 4.823 | 0.078 | 0.077 | 0.090 | 0.118 | 0.195 | 3.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 28 | 28 | 27 | 36 | 26 | 26 | 26 | 133 | 24 |
N.S. |
1 | 0.85 | 0.85 | 0.82 | 1.09 | 0.79 | 0.79 | 0.79 | 4.03 | 0.73 |
time (sec) |
N/A | 0.706 | 0.053 | 0.947 | 0.317 | 0.090 | 0.187 | 0.641 | 0.223 | 5.317 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-1) | B | F(-1) | F(-1) | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 41 | 32 | 0 | 2650 | 0 | 0 | 5081 | 0 |
N.S. |
1 | 0.00 | 1.95 | 1.52 | 0.00 | 126.19 | 0.00 | 0.00 | 241.95 | 0.00 |
time (sec) |
N/A | 0.000 | 0.246 | 1.635 | 0.000 | 0.667 | 0.000 | 0.000 | 39.145 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 15 | 15 | 16 | 15 | 15 | 22 | 15 | 16 | 15 |
N.S. |
1 | 0.83 | 0.83 | 0.89 | 0.83 | 0.83 | 1.22 | 0.83 | 0.89 | 0.83 |
time (sec) |
N/A | 0.161 | 0.002 | 0.280 | 0.026 | 0.084 | 0.073 | 0.110 | 0.186 | 0.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 17 | 16 | 15 | 15 | 14 | 15 | 11 | 14 |
N.S. |
1 | 1.00 | 1.00 | 0.94 | 0.88 | 0.88 | 0.82 | 0.88 | 0.65 | 0.82 |
time (sec) |
N/A | 0.152 | 0.002 | 0.232 | 0.030 | 0.075 | 0.050 | 0.123 | 0.175 | 3.115 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | B | B | B | B | B | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 62 | 76 | 261 | 79 | 58 | 125 | 113 | 203 |
N.S. |
1 | 0.00 | 2.30 | 2.81 | 9.67 | 2.93 | 2.15 | 4.63 | 4.19 | 7.52 |
time (sec) |
N/A | 0.000 | 0.219 | 11.526 | 0.155 | 0.087 | 0.256 | 0.150 | 0.195 | 3.342 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 51 | 18 | 24 | 35 | 17 | 20 | 22 | 27 | 14 |
N.S. |
1 | 2.32 | 0.82 | 1.09 | 1.59 | 0.77 | 0.91 | 1.00 | 1.23 | 0.64 |
time (sec) |
N/A | 0.286 | 0.085 | 0.283 | 0.026 | 0.077 | 0.078 | 0.107 | 0.200 | 2.992 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | B | B | B | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 34 | 0 | 32 | 85 | 72 | 72 | 71 | 0 | 278 | 76 |
N.S. |
1 | 0.00 | 0.94 | 2.50 | 2.12 | 2.12 | 2.09 | 0.00 | 8.18 | 2.24 |
time (sec) |
N/A | 0.000 | 0.081 | 41.784 | 0.082 | 0.085 | 0.294 | 0.000 | 200.022 | 3.472 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 130 | 30 | 148 | 124 | 144 | 332 | 207 | 236 | 27 |
N.S. |
1 | 5.00 | 1.15 | 5.69 | 4.77 | 5.54 | 12.77 | 7.96 | 9.08 | 1.04 |
time (sec) |
N/A | 0.367 | 0.047 | 0.733 | 0.040 | 0.097 | 0.407 | 0.144 | 0.219 | 3.433 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | F | A | A | A | A | F | B | B |
verified |
N/A | Yes | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 31 | 0 | 32 | 31 | 32 | 27 | 0 | 31 | 31 |
N.S. |
1 | 1.00 | 0.00 | 1.03 | 1.00 | 1.03 | 0.87 | 0.00 | 1.00 | 1.00 |
time (sec) |
N/A | 0.416 | 0.000 | 27.358 | 0.181 | 0.082 | 1.543 | 0.000 | 0.191 | 3.856 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 35 | 33 | 31 | 30 | 29 | 54 | 31 | 30 | 92 | 31 |
N.S. |
1 | 0.94 | 0.89 | 0.86 | 0.83 | 1.54 | 0.89 | 0.86 | 2.63 | 0.89 |
time (sec) |
N/A | 0.483 | 0.020 | 0.319 | 0.026 | 0.079 | 0.530 | 0.113 | 0.185 | 3.021 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | B | F | F | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 25 | 25 | 40 | 39 | 39 | 41 | 0 | 404 | 43 |
N.S. |
1 | 0.96 | 0.96 | 1.54 | 1.50 | 1.50 | 1.58 | 0.00 | 15.54 | 1.65 |
time (sec) |
N/A | 1.289 | 0.634 | 1.474 | 0.358 | 0.079 | 3.285 | 0.000 | 0.871 | 3.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F | F | B | A | F(-1) | F | B | F(-1) |
verified |
N/A | N/A | N/A | N/A | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 0 | 0 | 193 | 35 | 0 | 0 | 31 | 0 |
N.S. |
1 | 0.00 | 0.00 | 0.00 | 6.43 | 1.17 | 0.00 | 0.00 | 1.03 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 0.000 | 0.535 | 0.080 | 0.000 | 0.000 | 0.229 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 12 | 12 | 11 | 11 | 10 | 11 | 12 | 11 |
N.S. |
1 | 0.00 | 0.44 | 0.44 | 0.41 | 0.41 | 0.37 | 0.41 | 0.44 | 0.41 |
time (sec) |
N/A | 0.000 | 0.085 | 0.066 | 0.066 | 0.082 | 0.044 | 0.118 | 0.185 | 0.039 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 26 | 14 | 14 | 48 | 16 | 17 | 16 | 16 | 16 |
N.S. |
1 | 1.73 | 0.93 | 0.93 | 3.20 | 1.07 | 1.13 | 1.07 | 1.07 | 1.07 |
time (sec) |
N/A | 0.189 | 0.067 | 0.125 | 0.078 | 0.078 | 0.048 | 0.113 | 0.177 | 3.207 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | B | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 184 | 35 | 171 | 155 | 149 | 196 | 229 | 223 | 44 |
N.S. |
1 | 7.08 | 1.35 | 6.58 | 5.96 | 5.73 | 7.54 | 8.81 | 8.58 | 1.69 |
time (sec) |
N/A | 0.502 | 0.068 | 1.430 | 0.125 | 0.098 | 0.968 | 0.136 | 0.210 | 3.303 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 43 | 33 | 33 | 23 | 33 | 31 | 29 | 36 | 32 |
N.S. |
1 | 1.54 | 1.18 | 1.18 | 0.82 | 1.18 | 1.11 | 1.04 | 1.29 | 1.14 |
time (sec) |
N/A | 0.725 | 1.891 | 2.721 | 0.178 | 0.089 | 29.937 | 0.238 | 8.982 | 3.310 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 20 | 19 | 18 | 23 | 28 | 15 | 22 | 38 | 18 |
N.S. |
1 | 1.00 | 0.95 | 0.90 | 1.15 | 1.40 | 0.75 | 1.10 | 1.90 | 0.90 |
time (sec) |
N/A | 0.326 | 0.060 | 0.194 | 0.064 | 0.082 | 0.061 | 0.111 | 0.187 | 2.929 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 19 | 16 | 17 | 11 | 16 | 15 | 11 | 18 | 13 |
N.S. |
1 | 0.70 | 0.59 | 0.63 | 0.41 | 0.59 | 0.56 | 0.41 | 0.67 | 0.48 |
time (sec) |
N/A | 0.353 | 0.028 | 0.116 | 0.089 | 0.069 | 0.060 | 0.115 | 1.068 | 3.042 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | B | B | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 44 | 52 | 0 | 103 | 42 | 0 | 102 | 0 |
N.S. |
1 | 0.00 | 1.57 | 1.86 | 0.00 | 3.68 | 1.50 | 0.00 | 3.64 | 0.00 |
time (sec) |
N/A | 0.000 | 0.073 | 83.609 | 0.000 | 0.101 | 106.546 | 0.000 | 32.015 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 17 | 22 | 14 | 13 | 13 | 15 | 14 | 13 | 13 |
N.S. |
1 | 1.00 | 1.29 | 0.82 | 0.76 | 0.76 | 0.88 | 0.82 | 0.76 | 0.76 |
time (sec) |
N/A | 0.159 | 0.007 | 0.098 | 0.029 | 0.072 | 0.033 | 0.126 | 0.173 | 2.931 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 30 | 18 | 30 | 17 | 14 | 24 | 35 | 19 |
N.S. |
1 | 0.00 | 1.58 | 0.95 | 1.58 | 0.89 | 0.74 | 1.26 | 1.84 | 1.00 |
time (sec) |
N/A | 0.000 | 2.505 | 0.181 | 0.088 | 0.076 | 0.074 | 0.127 | 0.180 | 3.140 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 18 | 28 | 20 | 18 | 34 | 15 | 29 | 36 | 15 |
N.S. |
1 | 0.78 | 1.22 | 0.87 | 0.78 | 1.48 | 0.65 | 1.26 | 1.57 | 0.65 |
time (sec) |
N/A | 0.252 | 0.012 | 0.279 | 0.031 | 0.075 | 0.117 | 0.115 | 0.169 | 0.062 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 37 | 33 | 32 | 42 | 36 | 0 | 36 | 32 |
N.S. |
1 | 0.00 | 1.23 | 1.10 | 1.07 | 1.40 | 1.20 | 0.00 | 1.20 | 1.07 |
time (sec) |
N/A | 0.000 | 0.106 | 5.407 | 0.095 | 0.092 | 0.167 | 0.000 | 0.172 | 3.073 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 10 | 12 | 11 | 10 | 10 | 7 | 11 | 10 | 10 |
N.S. |
1 | 0.59 | 0.71 | 0.65 | 0.59 | 0.59 | 0.41 | 0.65 | 0.59 | 0.59 |
time (sec) |
N/A | 0.153 | 0.002 | 0.088 | 0.026 | 0.078 | 0.031 | 0.124 | 0.191 | 2.934 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 19 | 16 | 17 | 17 | 17 | 22 | 17 | 15 | 14 |
N.S. |
1 | 1.27 | 1.07 | 1.13 | 1.13 | 1.13 | 1.47 | 1.13 | 1.00 | 0.93 |
time (sec) |
N/A | 0.484 | 0.029 | 0.296 | 0.064 | 0.078 | 0.050 | 0.122 | 0.171 | 3.005 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F | A | A | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 19 | 34 | 0 | 33 | 36 | 29 | 28 | 0 |
N.S. |
1 | 0.00 | 0.90 | 1.62 | 0.00 | 1.57 | 1.71 | 1.38 | 1.33 | 0.00 |
time (sec) |
N/A | 0.000 | 5.061 | 7.793 | 0.000 | 0.099 | 0.341 | 0.279 | 0.181 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 20 | 26 | 30 | 25 | 19 | 25 | 77 | 22 |
N.S. |
1 | 0.83 | 0.83 | 1.08 | 1.25 | 1.04 | 0.79 | 1.04 | 3.21 | 0.92 |
time (sec) |
N/A | 4.513 | 0.108 | 0.852 | 0.106 | 0.088 | 0.093 | 0.138 | 0.174 | 3.233 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 13 | 17 | 21 | 15 | 17 | 17 | 15 | 17 | 15 | 18 |
N.S. |
1 | 1.31 | 1.62 | 1.15 | 1.31 | 1.31 | 1.15 | 1.31 | 1.15 | 1.38 |
time (sec) |
N/A | 0.138 | 0.002 | 0.070 | 0.025 | 0.070 | 0.018 | 0.108 | 0.178 | 3.169 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 0 | 17 | 21 | 22 | 20 | 14 | 345 | 19 | 167 |
N.S. |
1 | 0.00 | 0.89 | 1.11 | 1.16 | 1.05 | 0.74 | 18.16 | 1.00 | 8.79 |
time (sec) |
N/A | 0.000 | 0.154 | 2.181 | 0.183 | 0.084 | 0.098 | 0.268 | 0.179 | 3.863 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 15 | 15 | 13 | 12 | 12 | 12 | 12 | 13 | 12 |
N.S. |
1 | 1.00 | 1.00 | 0.87 | 0.80 | 0.80 | 0.80 | 0.80 | 0.87 | 0.80 |
time (sec) |
N/A | 0.199 | 0.004 | 0.179 | 0.029 | 0.077 | 0.047 | 0.106 | 0.174 | 0.188 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | F | A | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 81 | 31 | 38 | 0 | 36 | 39 | 65 | 44 | 31 |
N.S. |
1 | 3.00 | 1.15 | 1.41 | 0.00 | 1.33 | 1.44 | 2.41 | 1.63 | 1.15 |
time (sec) |
N/A | 0.375 | 1.915 | 0.376 | 0.000 | 0.082 | 0.087 | 0.114 | 0.171 | 0.076 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 36 | 37 | 49 | 48 | 32 | 51 | 45 | 76 |
N.S. |
1 | 0.00 | 1.29 | 1.32 | 1.75 | 1.71 | 1.14 | 1.82 | 1.61 | 2.71 |
time (sec) |
N/A | 0.000 | 0.353 | 1.306 | 0.163 | 0.087 | 0.106 | 0.197 | 0.173 | 3.646 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 36 | 85 | 46 | 37 | 48 | 48 | 60 | 48 | 70 | 48 |
N.S. |
1 | 2.36 | 1.28 | 1.03 | 1.33 | 1.33 | 1.67 | 1.33 | 1.94 | 1.33 |
time (sec) |
N/A | 0.345 | 0.875 | 0.827 | 0.040 | 0.090 | 0.090 | 0.134 | 0.177 | 3.100 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | B | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 39 | 24 | 48 | 33 | 31 | 67 | 60 | 65 |
N.S. |
1 | 0.00 | 1.22 | 0.75 | 1.50 | 1.03 | 0.97 | 2.09 | 1.88 | 2.03 |
time (sec) |
N/A | 0.000 | 3.702 | 2.401 | 18.035 | 0.086 | 0.322 | 0.142 | 0.582 | 3.553 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | F(-1) | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 0 | 34 | 24 | 31 | 48 | 0 | 0 | 364 | 61 |
N.S. |
1 | 0.00 | 1.06 | 0.75 | 0.97 | 1.50 | 0.00 | 0.00 | 11.38 | 1.91 |
time (sec) |
N/A | 0.000 | 3.986 | 2.653 | 0.080 | 0.098 | 0.000 | 0.000 | 0.179 | 0.125 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 18 | 14 | 13 | 12 | 17 | 12 | 12 | 17 | 12 |
N.S. |
1 | 1.29 | 1.00 | 0.93 | 0.86 | 1.21 | 0.86 | 0.86 | 1.21 | 0.86 |
time (sec) |
N/A | 0.274 | 0.005 | 0.524 | 0.022 | 0.083 | 0.060 | 0.122 | 0.184 | 3.129 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | A | A | B | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 42 | 27 | 26 | 125 | 18 | 24 | 25 | 47 | 18 |
N.S. |
1 | 2.21 | 1.42 | 1.37 | 6.58 | 0.95 | 1.26 | 1.32 | 2.47 | 0.95 |
time (sec) |
N/A | 0.338 | 0.043 | 0.530 | 0.036 | 0.080 | 0.071 | 0.114 | 0.173 | 3.493 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | F(-1) | A | F(-1) | B | A | F(-2) | F | F(-1) |
verified |
N/A | N/A | N/A | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 38 | 0 | 0 | 71 | 0 | 71 | 31 | 0 | 0 | 0 |
N.S. |
1 | 0.00 | 0.00 | 1.87 | 0.00 | 1.87 | 0.82 | 0.00 | 0.00 | 0.00 |
time (sec) |
N/A | 0.000 | 0.000 | 48.536 | 0.000 | 0.095 | 0.547 | 0.000 | 0.358 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | B | B | A | B | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 57 | 58 | 22 | 49 | 49 | 56 | 49 | 53 | 55 |
N.S. |
1 | 2.59 | 2.64 | 1.00 | 2.23 | 2.23 | 2.55 | 2.23 | 2.41 | 2.50 |
time (sec) |
N/A | 0.199 | 0.008 | 0.220 | 0.029 | 0.070 | 0.026 | 0.110 | 0.174 | 2.719 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 13 | 17 | 13 | 12 | 12 | 10 | 12 | 12 | 12 |
N.S. |
1 | 0.65 | 0.85 | 0.65 | 0.60 | 0.60 | 0.50 | 0.60 | 0.60 | 0.60 |
time (sec) |
N/A | 0.151 | 0.016 | 0.087 | 0.033 | 0.080 | 0.035 | 0.110 | 0.176 | 0.040 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-2) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 28 | 0 | 25 | 42 | 34 | 41 | 32 | 0 | 106 | 55 |
N.S. |
1 | 0.00 | 0.89 | 1.50 | 1.21 | 1.46 | 1.14 | 0.00 | 3.79 | 1.96 |
time (sec) |
N/A | 0.000 | 1.492 | 1.180 | 0.170 | 0.097 | 7.620 | 0.000 | 0.180 | 2.797 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | B | A | F(-2) | F | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 27 | 27 | 26 | 29 | 27 | 0 | 0 | 27 | 71 |
N.S. |
1 | 1.93 | 1.93 | 1.86 | 2.07 | 1.93 | 0.00 | 0.00 | 1.93 | 5.07 |
time (sec) |
N/A | 0.545 | 0.069 | 1.061 | 0.173 | 0.082 | 0.000 | 0.000 | 0.184 | 3.264 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | F(-2) | B | F(-2) | F | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 0 | 26 | 22 | 0 | 67 | 0 | 0 | 35 | 35 |
N.S. |
1 | 0.00 | 0.96 | 0.81 | 0.00 | 2.48 | 0.00 | 0.00 | 1.30 | 1.30 |
time (sec) |
N/A | 0.000 | 1.195 | 37.902 | 0.000 | 0.100 | 0.000 | 0.000 | 0.206 | 3.133 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | C | F | A | F(-1) | F | B | F(-1) |
verified |
N/A | N/A | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 24 | 261 | 0 | 25 | 0 | 0 | 27 | 0 |
N.S. |
1 | 0.00 | 0.96 | 10.44 | 0.00 | 1.00 | 0.00 | 0.00 | 1.08 | 0.00 |
time (sec) |
N/A | 0.000 | 5.415 | 0.695 | 0.000 | 0.102 | 0.000 | 0.000 | 0.178 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 13 | 21 | 15 | 14 | 14 | 12 | 14 | 23 | 144 |
N.S. |
1 | 0.93 | 1.50 | 1.07 | 1.00 | 1.00 | 0.86 | 1.00 | 1.64 | 10.29 |
time (sec) |
N/A | 0.296 | 0.047 | 0.229 | 0.182 | 0.072 | 0.051 | 0.116 | 0.181 | 3.065 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | No | TBD | TBD | TBD | TBD | TBD | TBD |
size | 14 | 17 | 13 | 11 | 10 | 14 | 8 | 14 | 15 | 10 |
N.S. |
1 | 1.21 | 0.93 | 0.79 | 0.71 | 1.00 | 0.57 | 1.00 | 1.07 | 0.71 |
time (sec) |
N/A | 0.166 | 0.003 | 0.105 | 0.030 | 0.077 | 0.051 | 0.111 | 0.176 | 2.767 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 8 | 4 | 4 | 5 | 4 | 4 | 3 | 5 | 4 | 4 |
N.S. |
1 | 0.50 | 0.50 | 0.62 | 0.50 | 0.50 | 0.38 | 0.62 | 0.50 | 0.50 |
time (sec) |
N/A | 0.123 | 0.000 | 0.031 | 0.034 | 0.067 | 0.020 | 0.109 | 0.179 | 0.006 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 20 | 16 | 23 | 20 | 24 | 23 | 32 | 25 |
N.S. |
1 | 0.00 | 0.91 | 0.73 | 1.05 | 0.91 | 1.09 | 1.05 | 1.45 | 1.14 |
time (sec) |
N/A | 0.000 | 0.496 | 0.332 | 0.165 | 0.090 | 0.203 | 0.129 | 0.179 | 0.079 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | B | C | A | A | F | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 0 | 25 | 50 | 94 | 28 | 27 | 0 | 48 | 0 |
N.S. |
1 | 0.00 | 1.09 | 2.17 | 4.09 | 1.22 | 1.17 | 0.00 | 2.09 | 0.00 |
time (sec) |
N/A | 0.000 | 0.465 | 3.042 | 0.285 | 0.087 | 0.395 | 0.000 | 0.177 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 29 | 28 | 28 | 27 | 27 | 28 | 27 | 26 | 28 | 26 |
N.S. |
1 | 0.97 | 0.97 | 0.93 | 0.93 | 0.97 | 0.93 | 0.90 | 0.97 | 0.90 |
time (sec) |
N/A | 3.452 | 0.067 | 60.737 | 0.102 | 0.082 | 0.710 | 0.711 | 0.217 | 3.242 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 20 | 22 | 22 | 22 | 26 | 20 | 15 | 590 | 18 | 20 |
N.S. |
1 | 1.10 | 1.10 | 1.10 | 1.30 | 1.00 | 0.75 | 29.50 | 0.90 | 1.00 |
time (sec) |
N/A | 0.449 | 0.019 | 8.921 | 0.255 | 0.078 | 0.155 | 2.505 | 0.175 | 3.376 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 20 | 20 | 24 | 35 | 24 | 20 | 24 | 23 | 199 |
N.S. |
1 | 0.83 | 0.83 | 1.00 | 1.46 | 1.00 | 0.83 | 1.00 | 0.96 | 8.29 |
time (sec) |
N/A | 0.627 | 0.188 | 1.464 | 0.204 | 0.084 | 0.101 | 1.148 | 0.173 | 3.347 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 32 | 34 | 55 | 35 | 34 | 48 | 37 | 35 | 63 | 34 |
N.S. |
1 | 1.06 | 1.72 | 1.09 | 1.06 | 1.50 | 1.16 | 1.09 | 1.97 | 1.06 |
time (sec) |
N/A | 0.255 | 0.031 | 0.379 | 0.034 | 0.093 | 0.187 | 0.115 | 0.168 | 0.099 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 20 | 18 | 21 | 18 | 20 | 17 | 20 | 22 | 18 |
N.S. |
1 | 1.05 | 0.95 | 1.11 | 0.95 | 1.05 | 0.89 | 1.05 | 1.16 | 0.95 |
time (sec) |
N/A | 0.262 | 0.048 | 0.543 | 0.091 | 0.083 | 0.093 | 0.130 | 0.174 | 2.909 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | B | A | B | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 26 | 0 | 31 | 32 | 30 | 31 | 63 | 34 | 32 | 0 |
N.S. |
1 | 0.00 | 1.19 | 1.23 | 1.15 | 1.19 | 2.42 | 1.31 | 1.23 | 0.00 |
time (sec) |
N/A | 0.000 | 5.048 | 1.668 | 0.080 | 0.082 | 0.208 | 0.148 | 0.173 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 19 | 13 | 13 | 12 | 11 | 11 | 8 | 11 | 16 | 11 |
N.S. |
1 | 0.68 | 0.68 | 0.63 | 0.58 | 0.58 | 0.42 | 0.58 | 0.84 | 0.58 |
time (sec) |
N/A | 0.178 | 0.008 | 0.060 | 0.030 | 0.078 | 0.051 | 0.117 | 0.177 | 0.031 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 30 | 23 | 20 | 20 | 26 | 22 | 26 | 23 |
N.S. |
1 | 0.00 | 1.36 | 1.05 | 0.91 | 0.91 | 1.18 | 1.00 | 1.18 | 1.05 |
time (sec) |
N/A | 0.000 | 0.068 | 0.223 | 0.236 | 0.083 | 0.550 | 0.109 | 0.194 | 3.163 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 23 | 32 | 32 | 29 | 26 | 32 | 29 | 30 | 53 | 34 |
N.S. |
1 | 1.39 | 1.39 | 1.26 | 1.13 | 1.39 | 1.26 | 1.30 | 2.30 | 1.48 |
time (sec) |
N/A | 0.497 | 0.371 | 0.680 | 0.242 | 0.081 | 0.137 | 0.213 | 0.177 | 3.018 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 15 | 8 | 17 | 7 | 8 | 8 | 7 | 13 | 7 | 6 |
N.S. |
1 | 0.53 | 1.13 | 0.47 | 0.53 | 0.53 | 0.47 | 0.87 | 0.47 | 0.40 |
time (sec) |
N/A | 0.135 | 0.003 | 0.109 | 0.026 | 0.083 | 0.044 | 0.112 | 0.180 | 2.992 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 21 | 0 | 17 | 18 | 24 | 17 | 19 | 0 | 29 | 25 |
N.S. |
1 | 0.00 | 0.81 | 0.86 | 1.14 | 0.81 | 0.90 | 0.00 | 1.38 | 1.19 |
time (sec) |
N/A | 0.000 | 5.031 | 1.810 | 0.161 | 0.090 | 0.931 | 0.000 | 0.181 | 3.082 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 18 | 21 | 18 | 18 | 18 | 18 | 20 | 21 | 21 | 17 |
N.S. |
1 | 1.17 | 1.00 | 1.00 | 1.00 | 1.00 | 1.11 | 1.17 | 1.17 | 0.94 |
time (sec) |
N/A | 0.170 | 0.004 | 0.479 | 0.036 | 0.073 | 0.131 | 0.108 | 0.170 | 0.094 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 17 | 13 | 13 | 14 | 13 | 15 | 12 | 13 | 13 | 13 |
N.S. |
1 | 0.76 | 0.76 | 0.82 | 0.76 | 0.88 | 0.71 | 0.76 | 0.76 | 0.76 |
time (sec) |
N/A | 0.304 | 0.017 | 0.112 | 0.024 | 0.087 | 0.055 | 0.110 | 0.171 | 2.817 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | F | F(-1) |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 25 | 0 | 28 | 28 | 27 | 27 | 29 | 29 | 107 | 0 |
N.S. |
1 | 0.00 | 1.12 | 1.12 | 1.08 | 1.08 | 1.16 | 1.16 | 4.28 | 0.00 |
time (sec) |
N/A | 0.000 | 3.706 | 0.602 | 0.098 | 0.079 | 0.133 | 0.140 | 200.021 | 0.000 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | B | A | F(-1) | F(-1) | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 30 | 0 | 37 | 36 | 88 | 35 | 0 | 0 | 37 | 63 |
N.S. |
1 | 0.00 | 1.23 | 1.20 | 2.93 | 1.17 | 0.00 | 0.00 | 1.23 | 2.10 |
time (sec) |
N/A | 0.000 | 2.457 | 244.899 | 0.532 | 0.096 | 0.000 | 0.000 | 1.181 | 3.453 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 47 | 25 | 28 | 30 | 30 | 26 | 30 | 27 | 30 |
N.S. |
1 | 1.96 | 1.04 | 1.17 | 1.25 | 1.25 | 1.08 | 1.25 | 1.12 | 1.25 |
time (sec) |
N/A | 0.238 | 0.031 | 0.401 | 0.036 | 0.097 | 0.103 | 0.117 | 0.207 | 0.068 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | A | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 31 | 21 | 21 | 19 | 17 | 17 | 17 | 17 | 18 | 17 |
N.S. |
1 | 0.68 | 0.68 | 0.61 | 0.55 | 0.55 | 0.55 | 0.55 | 0.58 | 0.55 |
time (sec) |
N/A | 0.183 | 0.002 | 0.090 | 0.028 | 0.073 | 0.037 | 0.113 | 0.196 | 3.017 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 27 | 26 | 26 | 26 | 27 | 29 | 26 | 68 | 38 | 26 |
N.S. |
1 | 0.96 | 0.96 | 0.96 | 1.00 | 1.07 | 0.96 | 2.52 | 1.41 | 0.96 |
time (sec) |
N/A | 0.234 | 0.041 | 0.278 | 0.068 | 0.086 | 0.087 | 0.118 | 0.193 | 3.035 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | B | B | F | B | B | B | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 24 | 21 | 909 | 114 | 0 | 96 | 138 | 240 | 249 | 100 |
N.S. |
1 | 0.88 | 37.88 | 4.75 | 0.00 | 4.00 | 5.75 | 10.00 | 10.38 | 4.17 |
time (sec) |
N/A | 8.870 | 6.430 | 8.091 | 0.000 | 0.084 | 0.290 | 0.181 | 0.198 | 2.998 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | F | F | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 24 | 22 | 20 | 25 | 22 | 0 | 164 | 21 |
N.S. |
1 | 0.00 | 1.09 | 1.00 | 0.91 | 1.14 | 1.00 | 0.00 | 7.45 | 0.95 |
time (sec) |
N/A | 0.000 | 0.563 | 0.310 | 0.125 | 0.096 | 0.123 | 0.000 | 0.208 | 2.801 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | F | A | A | A | A | A | A | B | B |
verified |
N/A | N/A | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 22 | 0 | 29 | 29 | 33 | 32 | 29 | 28 | 35 | 28 |
N.S. |
1 | 0.00 | 1.32 | 1.32 | 1.50 | 1.45 | 1.32 | 1.27 | 1.59 | 1.27 |
time (sec) |
N/A | 0.000 | 4.500 | 0.172 | 0.063 | 0.097 | 0.139 | 0.124 | 0.188 | 0.084 |
Optimal | Rubi | MMA | Maple | Maxima | Fricas | Sympy | Giac | Reduce | Mupad | |
grade |
N/A | A | A | A | C | A | A | A | B | B |
verified |
N/A | Yes | Yes | Yes | TBD | TBD | TBD | TBD | TBD | TBD |
size | 33 | 42 | 23 | 20 | 130 | 29 | 27 | 21 | 32 | 21 |
N.S. |
1 | 1.27 | 0.70 | 0.61 | 3.94 | 0.88 | 0.82 | 0.64 | 0.97 | 0.64 |
time (sec) |
N/A | 0.354 | 0.047 | 0.367 | 0.107 | 0.083 | 0.514 | 0.116 | 0.202 | 0.076 |